Markov Chains Problem

I have come across a question that says market analysis has established that, on average, a new car is purchased every three years. Buying patterns are described by the matrix:

Large SmallLarge[ 60% 40% ]Small[ 25% 75% ]

Am I correct in saying that the probability matrix can be re-written as....

L SS = L [ 0.6 0.4 ] S [ 0.25 0.75 ]

In addition, how would I calculate the probability of someone owning a large car still owning a large car in eight years' time, considering that the problem itself deals with car purchases every three years on average?

There is some drift due to calculation accuracy, but if you worked P out more accurately you may have something workable. But there may well be a rigorous way to do this rather than my "hey, lets use Excel and see what we get" approach

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Re: Markov Chains Problem

It matters and it doesn't matter; after six years it doesn't matter because on average everyone will have a new car. But it terms of after 8 years, that the questionable part. Perhaps 99% of the population buys their car in that year.

Remember that we're only worrying about current large car owners who'll have a large car in eight years time.

I will try and fiddle with it because as long as the elements in each row add to 1, I can indicate what I did is correct.